Cardinal Josef Glemp, primate of Poland and critic of the Polish government's harsh treatment of some Roman Catholic priests, is due to visit Washington in mid-September and will "probably" meet with U.S. officials here, a State Department official said yesterday.

After four years of representing Poland's predominantly Roman Catholic population in the face of a tense and rigid Polish regime, Glemp has emerged with a reputation as a skillful intermediary. He will come to the United States at a time when U.S.-Polish relations are "as bad as ever" and contact between Washington and Warsaw is at a minimum, according to one State Department official.

Gen. Wojciech Jaruzelski, the Polish leader, is scheduled to arrive at the United Nations Sept. 24, the day Glemp is to leave for home. The general is scheduled to speak before the General Assembly Sept. 27. A State Department official said it is "unlikely" that the Polish leader will meet with U.S. officials during his four-day visit.

"Some 65 heads of state are coming to the U.N opening," the official said. "We just can't meet with all of them." This will be Jaruzelski's first visit to the United States.

The Polish-American Congress is organizing a demonstration in New York to protest the Jaruzelski visit, a spokesman there said. The congress, a voice of Americans of Polish origin, is based in Chicago.

The State Department official said that several recent examples of domestic repression in Poland and the expulsion of three U.S. diplomats earlier this year have further cooled relations between Warsaw and Washington.

Those ties were severely strained when Poland declared martial law in December 1981, and the Reagan administration responded with economic sanctions.

Glemp will travel in the United States from Sept. 17 to 24, a State Department official said, adding that Glemp's Washington itinerary has not been completed. Meetings between Glemp and President Reagan or Secretary of State George P. Shultz have been ruled out, a U.S. official said.

It is Glemp's first visit to the United States as primate of Poland. He traveled here once before as a priest but canceled a planned 1982 trip because of domestic concerns, an information officer at the U.S. Catholic Conference here said.

The Polish cardinal was invited by the president of the National Conference of Bishops, James W. Malone, who met with him in Poland in May, according to the U.S. Catholic Conference.

Glemp is planning to visit Cardinal John Kroll, archbishop of Philadelphia, among other church-related stops.

Church-state relations in Poland were severely strained last October by the killing by secret police agents of the Rev. Jerzy Popieluszko, a popular Polish Roman Catholic priest.

The slaying also cramped Glemp's tiptoe diplomacy of restraining more radical priests while sheltering an array of political activities under the church's wing. In June, Glemp and Jaruzelski met for the first time to discuss difficulties between church and government.

Warsaw's expulsion of a U.S. defense attache in February struck a sour note in relations between Washington and Warsaw, and ties have remained bad, a State Department official said.

The official cited the recent convictions of three Solidarity members and two priests and the increase in political prisoners from 22 to 250 as examples of the deteriorating domestic situation in Poland.